School

University of Waterloo
Department

Statistics

Course Code

STAT231

Professor

Matthias Schonlau

Lecture

2

In General

•We have a model and data

•Goal: estimate parameter(s) of the model

•The likelihood method is a general method

that solves this problem.

•Likelihood inference has very good theoretical

properties. Those will be covered in Stat330

and Stat 450.

Likelihood function

•The likelihood is the probability that you observe

the data for specific parameter values

Where

– is the set of all possible parameter values

–D are random variables

–And d are realizations from those random variables

( ) Pr( ; ) LDd

Likelihood Method: in search of

parameter values

1. Define the likelihood function L()

–

2. Find the value for the parameter that

maximizes L()

–In practice we always maximize the log likelihood

3. The value that maximizes the likelihood, the

estimate of , is called the maximum

likelihood estimate

– for the Gaussian model

Over 90% improved by at least one letter grade.

OneClass has been such a huge help in my studies at UofT especially since I am a transfer student. OneClass is the study buddy I never had before and definitely gives me the extra push to get from a B to an A!

Leah — University of Toronto

Balancing social life With academics can be difficult, that is why I'm so glad that OneClass is out there where I can find the top notes for all of my classes. Now I can be the all-star student I want to be.

Saarim — University of Michigan

As a college student living on a college budget, I love how easy it is to earn gift cards just by submitting my notes.

Jenna — University of Wisconsin

OneClass has allowed me to catch up with my most difficult course! #lifesaver

Anne — University of California

Join OneClass

Access over 10 million pages of study

documents for 1.3 million courses.

Sign up

Join to view

OR

By registering, I agree to the
Terms
and
Privacy Policies

Already have an account?
Log in

Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.